Equality of

How would you set the thresholds?

Hover over the distributions and click anywhere to set the threshold.

Consider both the racial disparity and the tradeoff between true and false positive rates.

Wichita State University assigns each of its potential college applicants a score for how likely they are to enroll if given admission, based on attributes like sex, race, test scores, high school grades, and more. This score informs decisions on targeted advertising, admissions, and financial aid.

The score ranges from 0 to 100. The higher the score, the more likely it is that the student will enroll. Here is what the score distribution of 200 students would look like.

The prediction is not perfect. Some students with high scores may still end up dropping out of college.

And some students with low scores may still finish their degree if given admission.

To identify applicants who are likely to enroll, administrators use a threshold. Students who score above this threshold are classified as 'likely to enroll'.

An important thing to consider when setting the threshold is the true positive rate - the number of students who are classified as 'likely to enroll' out of all those who would actually enroll.

Lowering the threshold would result in a higher true positive rate, since we're marking more students as 'likely to enroll'.

However, doing so would also increase the false positive rate, meaning more students who would not actually enroll will be falsely classified as 'likely to enroll'. This is costly to the college and should be avoided.

Another major point of concern is the discrepancy between different demographic groups. In general, the software assigns more favorable scores to white students than black students.

Such disparate predictions represent a potentially true reflection of reality, as black students are historically 60% more likely to drop out of college than white students.


True Positivity

The third conception of fairness - Equality of Opportunity - would require that we equalize the true positive rates between the two groups [1]. Similar to Equality of Outcome, this involves modifying the thresholds to equalize a specific quantity. Here, instead of the overall prediction rate, that quantity is the true positive rate.

The model below has been modified to always equalize true positive rates among groups. Move one of the thresholds up or down and see how the other also moves to satisfy the equality requirement.


Opportunity vs. Outcome

Equality of Opportunity uses true positive rates as a tangible, quantifiable way to represent the somewhat abstract idea of opportunity. To calculate the true positive rate, we ask: out of all students who, if given admission, would enroll at Wichita (represented by the solid circle in the diagram below), how many were correctly predicted as so (the shaded area).

The true positive rate is calculated as the number of students in the shaded area divided by the number of those in the "would enroll" area. The denominator in this fraction plays a key role in our conceptualization of opportunity. We want to equalize rates among demographic groups, but that equalization is conditioned upon the ground truth - whether or not each student would enroll if given admission. Equalization of true positive rates would mean that if a student would enroll, then they should be as likely to be predicted as so as their peers from other demographic groups. Equalization of the prediction rates, which is what Equality of Outcome requires, does the same thing but without the "if" phrase [2].


Moral Desert

The conceptual difference between outcomes and opportunity touches at the oft-discussed idea of moral desert [3][4]. We say that a student who works hard deserves high grades and acceptance into good schools. Likewise, a person who commits a crime deserve proportional punishment for that crime. Equality of Opportunity distinguishes itself by asserting that the model should only give out positive predictions to those who deserve them.

However, "A deserves X" is usually a blanket statement that warrant further exploration and justification. How exactly is A entitled to X? What theoretical framework could underlie such entitlement?

One way to approach this is to take the perspective of the decision-makers. Admissions officers want to admit students who are likely to enroll and likely to succeed at their school. Banks want to give out loans to those who are likely to pay off those loans. Decision-makers get to decide who is deserving of the benefits that they want to distribute. This approach works for cases where the decision-maker has an unbiased interest in who to select. However, it fails to offer a substantive account of desert. Rather, it offers a purely descriptive criterion: whoever the decision-maker thinks is worthy or deserving of X is in fact worthy or deserving of it.

Another more substantive approach explores the "good" nature of moral, intellectual, and physical excellence. A virtuous citizen deserves praise and respect because we need to promote virtues and moral discipline. The need for such promotion may derive from the intrinsically "good" nature of virtues or the utilitarian need for social order. A hard-working student deserves high grades because high grades help promote intellectual excellence, which is desirable at educational institutions. The promotion of excellence is a more substantive account of desert. Still, it opens up a host of other, more tricky questions, such as what constitutes goodness and why it is desirable. This by no means undermines the excellence approach. Rather, it is an inevitable consequence of a substantive inquiry into what we often assume to the true.

Many share the intuition that Equality of Opportunity is a better conception of fairness than Equality of Outcome because it takes into account the idea of moral desert. We want to give positive predictions only to those who deserve them, not everyone. However, if our discussion on the nature of moral desert has shown anything, it's that we need to put more thought into systemizing and verifying our initial intuitions about what is fair and what is good.


Moving Forward

Three chapters, three conceptions of what fairness requires. Decision-making algorithms may seem inherently impartial since fundamentally they are logical systems that behave according to predetermined rules. However, the real world is full of biases and inequalities, and those biases/inequalities may leak into even the most logical of systems. We may address this issue by enforcing a strict non-awareness protocol (Blinding), equalizing the outcomes (Equality of Outcome) or the opportunity to receive positive outcomes (Equality of Opportunity).

Each conception has its pros and cons. Each touches on different theories about fairness, moral worth, and even intrinsic goodness. It is up to all stakeholders, from algorithm designers to decision makers and the people affected by those decision, to balance the performance and fairness constraints when constructing and approving a model that is suitable for their needs.

The stories and discussions in the these few chapters merely serve as starting points for more critical exanimations of how algorithmic models work and how we might make them more fair. Intuitions abound. It is easy to develop an initial reaction to a proposed conception of fairness. Such reactions may be biased given our differing backgrounds and experiences. To combat this, we must ask ourselves: what principles might justify and drive one approach over another? What, in turn, makes those principles sound, desirable, and generalizable?